I want to write article about frameworks like ROS and industrial control operating systems. One of my chapters must contains some mathematical that uses from calculating trajectory. Is there is the way to get math formulas that has been used in MoveIt while calculating movements?
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MoveIt is a big ROS package. By default, it uses the OMPL library to do the motion planning. Within Moveit, many different planners from OMPL are accessible (RRT, RRT*, PRM, etc). So if you want mathematical formulas, you'll first need to look for the planner you've been using with MoveIt, and then look for detailed information about it on the web.